Step by step
The question
Question: work out (2.5 × 10⁻³) × (4 × 10⁵).
(2.5 × 10−3) × (4 × 105)
1 Group the parts
Times can go in any order.
So we put the numbers together, and the powers of 10 together.
= 2.5 × 4 × 10−3 × 105
2 Work out each part
2.5 times 4 is 10.
2.5 × 4 = 10
We write 10 for the numbers.
= 10 × 10−3 × 105
The rule: same base, times, add the powers.
−3 plus 5 is 2.
10−3 × 105 = 10−3 + 5 = 102
Now we have 10 × 10².
= 10 × 102
3 Fix the number
10 is not under 10.
10 is 1 times 10, that is 1 × 10¹.
10 = 1 × 101
We write 1 × 10¹ in place of 10.
= 1 × 101 × 102
Add the powers: 1 plus 2 is 3.
101 × 102 = 101 + 2 = 103
So the answer is 1 × 10³.
= 1 × 103
4 Check
Let's check the answer is in scientific notation.
1 is from 1 to under 10, and it is times a power of 10.
Yes!
1 is from 1 to under 10, times 103
Let's look back.
First: group the parts.
Then: work out each part.
Then: fix the number.
Last: check.
Answer
= 1 × 103